What are the solutions to the equation x^2-1/2 x+1/4 =0 ?

The solutions to the equation x^2-1/2 x+1/4 =0 are x= 1/4+i(sqrt(3))/4 ,x= 1/4-i(sqrt(3))/4

Find the zeros of x^2-1/2 x+1/4 =0

The zeros of x^2-1/2 x+1/4 =0 are x= 1/4+i(sqrt(3))/4 ,x= 1/4-i(sqrt(3))/4

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x^{2} - \frac{1}{2} x + \frac{1}{4} = 0

x = \frac{1}{4} + i \frac{3}{4}, x = \frac{1}{4} - i \frac{3}{4}

Solution steps

x^{2} - \frac{1}{2} x + \frac{1}{4} = 0

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

x^{2} \cdot 4 - \frac{1}{2} x \cdot 4 + \frac{1}{4} \cdot 4 = 0 \cdot 4

Simplify

4 x^{2} - 2 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 4 \cdot 1}{2 \cdot 4}

Simplify

(- 2)^{2} - 4 \cdot 4 \cdot 1 : 23 i

x_{1, 2} = \frac{- ( - 2 ) \pm 2 3 i}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 3 i}{2 \cdot 4}, x_{2} = \frac{- ( - 2 ) - 2 3 i}{2 \cdot 4}

x = \frac{- ( - 2 ) + 2 3 i}{2 \cdot 4} : \frac{1}{4} + i \frac{3}{4}

x = \frac{- ( - 2 ) - 2 3 i}{2 \cdot 4} : \frac{1}{4} - i \frac{3}{4}

The solutions to the quadratic equation are:

x = \frac{1}{4} + i \frac{3}{4}, x = \frac{1}{4} - i \frac{3}{4}

4 - x^{2} = 60

2 (x + 2)^{2} + 5 = 12

2 n^{2} - 7 n - 21 = 0

(2 m - 1) x^{2} + m x + 15 = 0

2 - x (x + 4) = - 1 (x - 2)

What are the solutions to the equation x^2-1/2 x+1/4 =0 ?
The solutions to the equation x^2-1/2 x+1/4 =0 are x= 1/4+i(sqrt(3))/4 ,x= 1/4-i(sqrt(3))/4
Find the zeros of x^2-1/2 x+1/4 =0
The zeros of x^2-1/2 x+1/4 =0 are x= 1/4+i(sqrt(3))/4 ,x= 1/4-i(sqrt(3))/4